Nondeterminism in the Presence of a Diverse or Unknown Future

Choices made by nondeterministic word automata depend on both the past (the prefix of the word read so far) and the future (the suffix yet to be read). In several applications, most notably synthesis, the future is diverse or unknown, leading to algorithms that are based on deterministic automata. Hoping to retain some of the advantages of nondeterministic automata, researchers have studied restricted classes of nondeterministic automata. Three such classes are nondeterministic automata that are good for trees (GFT; i.e., ones that can be expanded to tree automata accepting the derived tree languages, thus whose choices should satisfy diverse futures), good for games (GFG; i.e., ones whose choices depend only on the past), and determinizable by pruning (DBP; i.e., ones that embody equivalent deterministic automata). The theoretical properties and relative merits of the different classes are still open, having vagueness on whether they really differ from deterministic automata. In particular, while DBP ⊆ GFG ⊆ GFT, it is not known whether every GFT automaton is GFG and whether every GFG automaton is DBP. Also open is the possible succinctness of GFG and GFT automata compared to deterministic automata. We study these problems for ω-regular automata with all common acceptance conditions. We show that GFT=GFG⊃DBP, and describe a determinization construction for GFG automata

Exploiting the Temporal Logic Hierarchy and the Non-Confluence Property for Efficient LTL Synthesis

The classic approaches to synthesize a reactive system from a linear temporal logic (LTL) specification first translate the given LTL formula to an equivalent omega-automaton and then compute a winning strategy for the corresponding omega-regular game. To this end, the obtained omega-automata have to be (pseudo)-determinized where typically a variant of Safra's determinization procedure is used. In this paper, we show that this determinization step can be significantly improved for tool implementations by replacing Safra's determinization by simpler determinization procedures. In particular, we exploit (1) the temporal logic hierarchy that corresponds to the well-known automata hierarchy consisting of safety, liveness, Buechi, and co-Buechi automata as well as their boolean closures, (2) the non-confluence property of omega-automata that result from certain translations of LTL formulas, and (3) symbolic implementations of determinization procedures for the Rabin-Scott and the Miyano-Hayashi breakpoint construction. In particular, we present convincing experimental results that demonstrate the practical applicability of our new synthesis procedure

On the Relative Succinctness of Nondeterministic Büchi and co-Büchi Word Automata

Abstract. The practical importance of automata on infinite objects has motivated a re-examination of the complexity of automata-theoretic constructions. One such construction is the translation, when possible, of nondeterministic Büchi word automata (NBW) to nondeterministic co-Büchi word automata (NCW). Among other applications, it is used in the translation (when possible) of LTL to the alternation-free µ-calculus. The best known upper bound for the translation of NBW to NCW is exponential (given an NBW with n states, the best translation yields an equivalent NCW with 2 O(n log n) states). On the other hand, the best known lower bound is trivial (no NBW with n states whose equivalent NCW requires even n+1 states is known). In fact, only recently was it shown that there is an NBW whose equivalent NCW requires a different structure. In this paper we improve the lower bound by showing that for every integer k ≥ 1 there is a language Lk over a two-letter alphabet, such that Lk can be recognized by an NBW with 2k+1 states, whereas the minimal NCW that recognizes Lk has 3k states. Even though this gap is not asymptotically very significant, it nonetheless demonstrates for the first time that NBWs are more succinct than NCWs. In addition, our proof points to a conceptual advantage of the Büchi condition: an NBW can abstract precise counting by counting to infinity with two states. To complete the picture, we consider also the reverse NCW to NBW translation, and show that the known upper bound, which duplicates the state space, is tight.

Synthesis of persistent systems. In Proc. 35rd International Conference on Application and Theory of Petri Nets and Concurrency (Tunis, August 2014), G. Ciardo, E. Kindler (eds.)

This paper presents efficient, specialised synthesis and reengineering algorithms for the case that a transition system is finite, persistent and reversible. It also shows by means of a complex example that structural properties of the synthesised Petri nets may not necessarily be entailed.SCOPUS: cp.kinfo:eu-repo/semantics/publishe